{
 "cells": [
  {
   "cell_type": "code",
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2025-01-03T08:39:53.905041Z",
     "start_time": "2025-01-03T08:39:53.900038Z"
    }
   },
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.random.seed(42) # 设置随机种子，以便结果可以复现\n",
    "# 创建用于训练的X矩阵，100行一列的数组\n",
    "X = 2 * np.random.rand(100, 1)\n",
    "print(len(X))\n"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100\n"
     ]
    }
   ],
   "execution_count": 8
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:39:53.969041Z",
     "start_time": "2025-01-03T08:39:53.964039Z"
    }
   },
   "cell_type": "code",
   "source": "X",
   "id": "a9fb85b0442ef8d1",
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "       [0.1271167 ],\n",
       "       [0.62196464],\n",
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       "       [1.45921236],\n",
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       "       [1.77442549],\n",
       "       [0.94442985],\n",
       "       [0.23918849],\n",
       "       [1.42648957],\n",
       "       [1.5215701 ],\n",
       "       [1.1225544 ],\n",
       "       [1.54193436],\n",
       "       [0.98759119],\n",
       "       [1.04546566],\n",
       "       [0.85508204],\n",
       "       [0.05083825],\n",
       "       [0.21578285]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 9
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:39:53.999038Z",
     "start_time": "2025-01-03T08:39:53.979039Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 接下来人为的设置真实的Y一列（y_hat），这里的4其实就是我们把W1=4，然后5就是W0=5\n",
    "# y = 5 + 4 * X \n",
    "y = 5 + 4 * X + np.random.randn(100, 1)\n",
    "\"\"\"\n",
    "np.random.randn(100, 1)是设置 error，因为 randn 是标准正太分布，\n",
    "符合我们前面讲过的误差服从均值为0的正太分布，\n",
    "这就意味着这样构建的X和Y的关系去使用我们前面讲过的多元线性回归去拟合求解会很合适。\n",
    "\"\"\"\n",
    "\"\"\"\n",
    "同时，我们有100个真实值y，我们有5+4X就是100个y_hat，\n",
    "那么我们的误差就是真实值减去预测值也会有100个误差值。\n",
    "所以这也就是我们去用randn去创建100行1列的误差数组的原因。\n",
    "\"\"\"\n",
    "\n",
    "y\n"
   ],
   "id": "bffd13c37e8d5536",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 8.08336802],\n",
       "       [12.3067071 ],\n",
       "       [10.94771231],\n",
       "       [ 7.80169896],\n",
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       "       [ 6.60506873],\n",
       "       [ 6.94256294],\n",
       "       [11.41113895],\n",
       "       [ 9.00042649],\n",
       "       [10.16282358],\n",
       "       [ 6.08007807],\n",
       "       [13.08802993],\n",
       "       [11.12978092],\n",
       "       [ 7.21198032],\n",
       "       [ 6.55167729],\n",
       "       [ 7.43588107],\n",
       "       [ 6.73188485],\n",
       "       [ 8.87038931],\n",
       "       [ 8.063452  ],\n",
       "       [ 5.86631817],\n",
       "       [10.19094343],\n",
       "       [ 6.37700616],\n",
       "       [ 7.34227064],\n",
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       "       [ 6.5387708 ],\n",
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       "       [ 7.49714036],\n",
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       "       [10.28150325],\n",
       "       [ 8.82276729],\n",
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       "       [ 6.41793098],\n",
       "       [13.02649625],\n",
       "       [ 7.8612718 ],\n",
       "       [ 9.39079082],\n",
       "       [ 8.89648292],\n",
       "       [ 7.75869311],\n",
       "       [ 9.96053933],\n",
       "       [ 8.66929127],\n",
       "       [11.7661407 ],\n",
       "       [10.63476486],\n",
       "       [12.6156429 ],\n",
       "       [11.65514315],\n",
       "       [ 8.2325364 ],\n",
       "       [12.44355685],\n",
       "       [ 4.6456363 ],\n",
       "       [ 7.04145533],\n",
       "       [ 4.44239408],\n",
       "       [ 9.15257705],\n",
       "       [ 7.32616503],\n",
       "       [ 6.84873074],\n",
       "       [12.44341729],\n",
       "       [ 6.6231623 ],\n",
       "       [ 7.47493601],\n",
       "       [10.64871142],\n",
       "       [ 4.51991057],\n",
       "       [11.6022097 ],\n",
       "       [ 5.85628794],\n",
       "       [13.67691836],\n",
       "       [ 9.94100744],\n",
       "       [ 5.26926884],\n",
       "       [ 5.5661185 ],\n",
       "       [11.8206761 ],\n",
       "       [10.9053516 ],\n",
       "       [11.17850555],\n",
       "       [10.49013805],\n",
       "       [ 5.82461091],\n",
       "       [ 8.1607983 ],\n",
       "       [ 5.21260106],\n",
       "       [13.77060192],\n",
       "       [10.46021794],\n",
       "       [ 6.4558807 ],\n",
       "       [ 6.16502041],\n",
       "       [ 6.5131769 ],\n",
       "       [ 8.38855118],\n",
       "       [11.99544501],\n",
       "       [ 9.27977745],\n",
       "       [13.06107807],\n",
       "       [ 9.19050033],\n",
       "       [ 6.77881413],\n",
       "       [12.60275128],\n",
       "       [10.84089227],\n",
       "       [ 8.73648142],\n",
       "       [10.27822301],\n",
       "       [ 8.13455449],\n",
       "       [ 9.10476093],\n",
       "       [ 8.76148012],\n",
       "       [ 5.48004381],\n",
       "       [ 6.69031466]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 10
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:39:54.015041Z",
     "start_time": "2025-01-03T08:39:54.000039Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# np.ones((100, 1))：创建了一个形状为 (100, 1) 的数组，数组中的所有元素都为1。\n",
    "# np.c_[]：按列连接数组\n",
    "\n",
    "X_b = np.c_[np.ones((100, 1)), X]\n",
    "X_b\n"
   ],
   "id": "f57431a880aaecda",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.74908024],\n",
       "       [1.        , 1.90142861],\n",
       "       [1.        , 1.46398788],\n",
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       "       [1.        , 0.58245828],\n",
       "       [1.        , 1.22370579],\n",
       "       [1.        , 0.27898772],\n",
       "       [1.        , 0.5842893 ],\n",
       "       [1.        , 0.73272369],\n",
       "       [1.        , 0.91213997],\n",
       "       [1.        , 1.57035192],\n",
       "       [1.        , 0.39934756],\n",
       "       [1.        , 1.02846888],\n",
       "       [1.        , 1.18482914],\n",
       "       [1.        , 0.09290083],\n",
       "       [1.        , 1.2150897 ],\n",
       "       [1.        , 0.34104825],\n",
       "       [1.        , 0.13010319],\n",
       "       [1.        , 1.89777107],\n",
       "       [1.        , 1.93126407],\n",
       "       [1.        , 1.6167947 ],\n",
       "       [1.        , 0.60922754],\n",
       "       [1.        , 0.19534423],\n",
       "       [1.        , 1.36846605],\n",
       "       [1.        , 0.88030499],\n",
       "       [1.        , 0.24407647],\n",
       "       [1.        , 0.99035382],\n",
       "       [1.        , 0.06877704],\n",
       "       [1.        , 1.8186408 ],\n",
       "       [1.        , 0.51755996],\n",
       "       [1.        , 1.32504457],\n",
       "       [1.        , 0.62342215],\n",
       "       [1.        , 1.04013604],\n",
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       "       [1.        , 0.176985  ],\n",
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       "       [1.        , 0.54269806],\n",
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       "       [1.        , 1.97377387],\n",
       "       [1.        , 1.54448954],\n",
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       "       [1.        , 1.45801434],\n",
       "       [1.        , 1.54254069],\n",
       "       [1.        , 0.1480893 ],\n",
       "       [1.        , 0.71693146],\n",
       "       [1.        , 0.23173812],\n",
       "       [1.        , 1.72620685],\n",
       "       [1.        , 1.24659625],\n",
       "       [1.        , 0.66179605],\n",
       "       [1.        , 0.1271167 ],\n",
       "       [1.        , 0.62196464],\n",
       "       [1.        , 0.65036664],\n",
       "       [1.        , 1.45921236],\n",
       "       [1.        , 1.27511494],\n",
       "       [1.        , 1.77442549],\n",
       "       [1.        , 0.94442985],\n",
       "       [1.        , 0.23918849],\n",
       "       [1.        , 1.42648957],\n",
       "       [1.        , 1.5215701 ],\n",
       "       [1.        , 1.1225544 ],\n",
       "       [1.        , 1.54193436],\n",
       "       [1.        , 0.98759119],\n",
       "       [1.        , 1.04546566],\n",
       "       [1.        , 0.85508204],\n",
       "       [1.        , 0.05083825],\n",
       "       [1.        , 0.21578285]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 11
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "根据公式：\n",
    "$$\n",
    "\\theta=\\left(X^TX\\right)^{-1}X^Ty\n",
    "$$"
   ],
   "id": "adf0ae7bd12da744"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:39:54.031039Z",
     "start_time": "2025-01-03T08:39:54.021039Z"
    }
   },
   "cell_type": "code",
   "source": [
    "\"\"\"\n",
    ".T就是transpose转置的作用\n",
    "dot就是向量点乘\n",
    "np.linalg.inv是矩阵求逆\n",
    "\"\"\"\n",
    "\"\"\"\n",
    "我们计算结果很有意思，就是你会发现最后并不能准确的计算出来5和4，\n",
    "而是计算出来一个接近期望的值，为什么？\n",
    "如果是我们给y不设定误差项，那么计算出来的结果是5和4\n",
    "\"\"\"\n",
    "theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)\n",
    "# 第一个数字是W0=5，第二个数字是W1=4\n",
    "theta_best\n"
   ],
   "id": "fd0f3d877c838c98",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5.21509616],\n",
       "       [3.77011339]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 12
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:39:54.046136Z",
     "start_time": "2025-01-03T08:39:54.041039Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 下面我们去把model模型使用起来，只有model模型预测的准，那么才有价值\n",
    "X_new = np.array([[0], [2]])\n",
    "X_new_b = np.c_[(np.ones((2, 1))), X_new]\n",
    "X_new_b"
   ],
   "id": "b8c5c8b9e3237c66",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0.],\n",
       "       [1., 2.]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 13
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "$$\n",
    "\\hat{y}=X\\theta \n",
    "$$"
   ],
   "id": "c1d36240a3684653"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:39:54.077654Z",
     "start_time": "2025-01-03T08:39:54.058657Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 这里我们同样构建一个两行一列的新的X，然后给它添加上一列恒为1的X0\n",
    "y_predict = X_new_b.dot(theta_best)\n",
    "y_predict\n"
   ],
   "id": "a76863b840d7828d",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5.21509616],\n",
       "       [12.75532293]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 14
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "",
   "id": "98d7e46e34e33010"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:39:54.156655Z",
     "start_time": "2025-01-03T08:39:54.092654Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 计算的期望应该在10、4附近\n",
    "plt.plot(X_new, y_predict, 'r.')\n",
    "plt.plot(X_new, y_predict, 'r-')\n",
    "plt.plot(X, y, 'b.')\n",
    "plt.axis([-1, 5, 0, 25])\n",
    "plt.show()\n"
   ],
   "id": "47f9eb15481a0cc3",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 15
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:39:54.171658Z",
     "start_time": "2025-01-03T08:39:54.158655Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "352377a12f7320d4",
   "outputs": [],
   "execution_count": 15
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:39:54.187657Z",
     "start_time": "2025-01-03T08:39:54.173657Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "1f432500ba264ab5",
   "outputs": [],
   "execution_count": 15
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:39:54.203654Z",
     "start_time": "2025-01-03T08:39:54.190657Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 如果我们影响y的因有两个\n",
    "# 设置随机种子，以便结果可以复现\n",
    "np.random.seed(42)\n",
    "\n",
    "X1 = 2 * np.random.rand(100, 1)\n",
    "X2 = 3 * np.random.rand(100, 1)\n",
    "\n",
    "X_b = np.c_[np.ones((100, 1)), X1, X2]\n",
    "X_b"
   ],
   "id": "ccae11cf483a24f3",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.74908024, 0.09428756],\n",
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       "       [1.        , 1.19731697, 1.52571207],\n",
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       "       [1.        , 1.66488528, 2.78909296],\n",
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       "       [1.        , 0.36364993, 1.90021127],\n",
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       "       [1.        , 1.93126407, 2.82872911],\n",
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       "       [1.        , 1.65747502, 1.90058913],\n",
       "       [1.        , 0.71350665, 1.60732405],\n",
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       "       [1.        , 1.60439396, 0.55955553],\n",
       "       [1.        , 0.14910129, 0.12232542],\n",
       "       [1.        , 1.97377387, 1.77267883],\n",
       "       [1.        , 1.54448954, 2.03269309],\n",
       "       [1.        , 0.39743136, 0.04976349],\n",
       "       [1.        , 0.01104423, 1.53627917],\n",
       "       [1.        , 1.63092286, 0.67948733],\n",
       "       [1.        , 1.41371469, 1.93551837],\n",
       "       [1.        , 1.45801434, 0.52309929],\n",
       "       [1.        , 1.54254069, 2.07281321],\n",
       "       [1.        , 0.1480893 , 1.16020604],\n",
       "       [1.        , 0.71693146, 2.81018997],\n",
       "       [1.        , 0.23173812, 0.41256283],\n",
       "       [1.        , 1.72620685, 1.02319905],\n",
       "       [1.        , 1.24659625, 0.34042056],\n",
       "       [1.        , 0.66179605, 2.77408085],\n",
       "       [1.        , 0.1271167 , 2.63201806],\n",
       "       [1.        , 0.62196464, 0.77382488],\n",
       "       [1.        , 0.65036664, 1.97995214],\n",
       "       [1.        , 1.45921236, 2.4516666 ],\n",
       "       [1.        , 1.27511494, 1.66560243],\n",
       "       [1.        , 1.77442549, 1.58895174],\n",
       "       [1.        , 0.94442985, 0.72555687],\n",
       "       [1.        , 0.23918849, 0.2793083 ],\n",
       "       [1.        , 1.42648957, 2.69164727],\n",
       "       [1.        , 1.5215701 , 2.70125417],\n",
       "       [1.        , 1.1225544 , 1.89930437],\n",
       "       [1.        , 1.54193436, 1.01708937],\n",
       "       [1.        , 0.98759119, 1.04762872],\n",
       "       [1.        , 1.04546566, 2.17786704],\n",
       "       [1.        , 0.85508204, 2.69133078],\n",
       "       [1.        , 0.05083825, 2.66125927],\n",
       "       [1.        , 0.21578285, 2.33962664]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 16
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:39:54.218659Z",
     "start_time": "2025-01-03T08:39:54.205657Z"
    }
   },
   "cell_type": "code",
   "source": [
    "y = 5 + 4 * X1 + 3 * X2 + np.random.randn(100, 1)\n",
    "y"
   ],
   "id": "3c3543c7d4a10d6c",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 7.5991589 ],\n",
       "       [18.56566185],\n",
       "       [13.97822784],\n",
       "       [13.65205268],\n",
       "       [16.2820219 ],\n",
       "       [ 8.96541915],\n",
       "       [ 7.96681171],\n",
       "       [19.38592302],\n",
       "       [10.89342191],\n",
       "       [12.14448441],\n",
       "       [ 8.93103461],\n",
       "       [13.38958808],\n",
       "       [20.99019613],\n",
       "       [14.38457723],\n",
       "       [12.97729371],\n",
       "       [16.20717437],\n",
       "       [14.42159852],\n",
       "       [10.12344582],\n",
       "       [15.59907671],\n",
       "       [11.36810301],\n",
       "       [17.08468284],\n",
       "       [14.52192456],\n",
       "       [10.47587926],\n",
       "       [ 9.74854532],\n",
       "       [10.71297823],\n",
       "       [16.57891187],\n",
       "       [13.69486632],\n",
       "       [19.58061992],\n",
       "       [10.42755307],\n",
       "       [ 9.11117147],\n",
       "       [12.54616535],\n",
       "       [ 8.8456357 ],\n",
       "       [ 6.37573826],\n",
       "       [16.34362133],\n",
       "       [21.68448122],\n",
       "       [14.30317626],\n",
       "       [11.25923203],\n",
       "       [10.59370032],\n",
       "       [13.30001568],\n",
       "       [18.12365749],\n",
       "       [14.85242528],\n",
       "       [ 9.98171716],\n",
       "       [ 9.92352565],\n",
       "       [15.36778538],\n",
       "       [ 8.74994687],\n",
       "       [10.78588591],\n",
       "       [13.03797633],\n",
       "       [12.54168508],\n",
       "       [10.19477836],\n",
       "       [ 9.54743835],\n",
       "       [22.01412124],\n",
       "       [14.41092165],\n",
       "       [12.44237601],\n",
       "       [15.62586861],\n",
       "       [19.16908918],\n",
       "       [15.06727727],\n",
       "       [12.27220763],\n",
       "       [17.27517093],\n",
       "       [ 8.07144672],\n",
       "       [15.29215542],\n",
       "       [12.37346828],\n",
       "       [13.51293598],\n",
       "       [17.01639823],\n",
       "       [13.43496799],\n",
       "       [ 7.28725879],\n",
       "       [16.62247252],\n",
       "       [ 8.52905084],\n",
       "       [13.17811658],\n",
       "       [ 8.27803999],\n",
       "       [16.34586679],\n",
       "       [17.9622976 ],\n",
       "       [ 5.12630004],\n",
       "       [ 9.1810826 ],\n",
       "       [14.651104  ],\n",
       "       [16.52569388],\n",
       "       [11.32361043],\n",
       "       [16.67329871],\n",
       "       [ 9.75257308],\n",
       "       [15.5679291 ],\n",
       "       [ 7.38109956],\n",
       "       [15.01999641],\n",
       "       [10.35604636],\n",
       "       [18.11337085],\n",
       "       [14.03844001],\n",
       "       [ 7.78419064],\n",
       "       [13.72777731],\n",
       "       [17.53006276],\n",
       "       [15.94970041],\n",
       "       [16.07203641],\n",
       "       [10.83965358],\n",
       "       [ 7.29966616],\n",
       "       [19.64665531],\n",
       "       [17.9897465 ],\n",
       "       [14.85362946],\n",
       "       [13.74406025],\n",
       "       [11.43992171],\n",
       "       [17.48091799],\n",
       "       [16.8993022 ],\n",
       "       [11.92624688],\n",
       "       [13.79987328]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 17
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "$$\n",
    "\\theta=\\left(X^TX\\right)^{-1}X^Ty\n",
    "$$"
   ],
   "id": "afa2e98c084b7a14"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:39:54.234657Z",
     "start_time": "2025-01-03T08:39:54.220659Z"
    }
   },
   "cell_type": "code",
   "source": [
    "theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)\n",
    "# 第一个数字是W0=5，第二个数字是W1=4，第三个数字是W2=3\n",
    "theta_best"
   ],
   "id": "201fa72a9e09fb3e",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.91061004],\n",
       "       [3.82913734],\n",
       "       [3.23977047]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 18
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:42:20.032482Z",
     "start_time": "2025-01-03T08:42:20.011106Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 创建2个测试数据\n",
    "# X_new = np.array([[1, 2], [3, 4]])\n",
    "X_new = np.array([[0, 0], [2, 3]])\n",
    "X_new_b = np.c_[(np.ones((2, 1))), X_new]\n",
    "X_new_b"
   ],
   "id": "e29bf3d0e2ba21a7",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [1., 2., 3.]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 26
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "$$\n",
    "\\hat{y}=X\\theta \n",
    "$$"
   ],
   "id": "5d9938982c2a5854"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:42:20.423949Z",
     "start_time": "2025-01-03T08:42:20.407950Z"
    }
   },
   "cell_type": "code",
   "source": [
    "y_predict = X_new_b.dot(theta_best)\n",
    "y_predict"
   ],
   "id": "f94b8bcc425b594f",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.91061004],\n",
       "       [22.28819613]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 27
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:42:20.643520Z",
     "start_time": "2025-01-03T08:42:20.624520Z"
    }
   },
   "cell_type": "code",
   "source": [
    "display(X_new[:, 0])\n",
    "display(X_new[:, 1])"
   ],
   "id": "48f9dff7fba3aa67",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([0, 3])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 28
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "\n",
   "id": "790427a912795fdd"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:42:21.351132Z",
     "start_time": "2025-01-03T08:42:21.245131Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 绘制二元一次线性\n",
    "# 预测的点\n",
    "plt.plot(X_new[:, 0], y_predict, 'r.')\n",
    "plt.plot(X_new[:, 1], y_predict, 'r.')\n",
    "# 预测的线\n",
    "plt.plot(X_new[:, 0], y_predict, 'r-')\n",
    "plt.plot(X_new[:, 1], y_predict, 'r-')\n",
    "# 数据集的点\n",
    "plt.plot(X, y, 'b.')\n",
    "\n",
    "plt.axis([-1, 5, 0, 30])\n",
    "plt.show()"
   ],
   "id": "93749b466af73ba4",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 29
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:42:21.901698Z",
     "start_time": "2025-01-03T08:42:21.894717Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "fe1f508590468929",
   "outputs": [],
   "execution_count": 29
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:42:22.719245Z",
     "start_time": "2025-01-03T08:42:22.579226Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 3D绘图\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "# 绘制数据点\n",
    "ax.scatter(X1, X2, y, color='b', label='Data point')\n",
    "\n",
    "# 绘制预测面\n",
    "ax.plot_surface(X_new[:, 0], X_new[:, 1], y_predict, color='r', alpha=0.5)\n",
    "\n",
    "# 设置轴标签\n",
    "ax.set_xlabel('X1')\n",
    "ax.set_ylabel('X2')\n",
    "ax.set_zlabel('y')\n",
    "\n",
    "plt.legend()\n",
    "plt.show()\n"
   ],
   "id": "6e6e857536abc30",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 30
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:39:54.720349Z",
     "start_time": "2025-01-03T08:39:54.707352Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "7cac2c8391a28a29",
   "outputs": [],
   "execution_count": 23
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:39:54.735348Z",
     "start_time": "2025-01-03T08:39:54.722350Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "1a975ea4c92ece33",
   "outputs": [],
   "execution_count": 23
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-01-03T08:39:54.750355Z",
     "start_time": "2025-01-03T08:39:54.737351Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "23be97f2fb9a89fd",
   "outputs": [],
   "execution_count": 23
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
